Magnetohydrodynamics (MHD) is the physical-mathematical framework that
describes the dynamics of magnetic fields in electrically conducting
fluids, e.g., plasmas and ionized
gases [1]}, [2]}.
Indeed, the electrically charged particles moving in a plasma
generate an electromagnetic field that self-consistently interacts
with the fluid motion through the Lorentz force acting on such
particles.
The theoretical framework of MHD has widely been used to develop
predictive mathematical models, for example, in astrophysics (solar
wind and space weather [3]}, galactic
jets [4]}), geophysics (dynamo
theory [5]}), and nuclear fusion (design of
fusion reactors, ignition in inertial confinement
fusion [6]}, [7]}, [8]}).
Roughly speaking, MHD resorts on a strongly nonlinear coupling of a
fluid flow submodel and an electromagnetic one.
In a general setting, as the one considered in this work, the fluid
flow submodel is based on the incompressible Navier-Stokes equations
and the electromagnetic submodel on the Maxwell equations.
A thorough description of the MHD models, their variants, derivation,
and physical and mathematical properties can be found in many
textbooks and review papers,
e.g., [9]}, [10]}, [1]}, [2]}
just to mention a few.
